Q. Which expression is equivalent to 4−4×424−2?416161616−84−8
Apply Properties of Exponents: Simplify the expression using the properties of exponents.We have the expression 4−4×(4−2)/(42). According to the properties of exponents, when we multiply powers with the same base, we add the exponents, and when we divide powers with the same base, we subtract the exponents.
Combine Exponents in Numerator: Combine the exponents in the numerator.We have 4−4×4−2, which can be combined as 4(−4+−2) because we add the exponents when multiplying with the same base.4−4×4−2=4(−4+−2)=4−6.
Divide Numerator by Denominator: Divide the numerator by the denominator.Now we have 4−6/42. According to the properties of exponents, when we divide powers with the same base, we subtract the exponents.4−6/42=4−6−2=4−8.
Check Answer Choices: Check the answer choices to see which one matches our result.We have found that the expression simplifies to 4−8. Looking at the answer choices, we see that the equivalent expression is 4−8.
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